Question

The marketing manager of a firm that produces laundry products decides to test market a new laundry product in each of the firm's two sales regions. He wants to determine whether there will be a difference in mean sales per market per month between the two regions. A random sample of 13 supermarkets from Region 1 had mean sales of 72.7 with a standard deviation of 9. A random sample of 17 supermarkets from Region 2 had a mean sales of 84.9 with a standard deviation of 7.6. Does the test marketing reveal a difference in potential mean sales per market in Region 2? Let μ1 be the mean sales per market in Region 1 and μ2 be the mean sales per market in Region 2. Use a significance level of α=0.01 for the test. Assume that the population variances are not equal and that the two populations are normally distributed.

Step 1 of 4 : State the null and alternative hypotheses for the test. Step 2 of 4 : compute the value of the t test statistic. Round to 3 decimal places. step 3 of 4 : determine the decision rule for rejected the null hypothesis. round to 3 decimal places step 4 of 4 : state the tests conclusion

Answer 1

Step 1

The null and alternative hypothesis

Step 2

Test statistic

where

72.7

84.9

9

7.6

n1=13, n2=17

Thus

Step 3

Calculation for degrees of freedom

=92.7064

=4.2508

df = 92.7064/4.2508 = 21.8=22 ( rounding to whole number)

For 0.01 with df = 22 , two tailed critical value of t is

tc = 2.819 ( from t table)

Reject H0 if calculated value of t < -2.819 or t > 2.819

Step 4

Since t < -2.819

Reject H0

At 0.01 level of significance , there is sufficient evidence to conclude that mean is different between two regions.